Explain a way of subdividing a $$102 \times 102$$ square into 2007 non-overlapping squares of integral sides.

PLACEHOLDER ANSWER - the answer is a construction. Divide the square into a $$51 \times 51$$ grid of $$2 \times 2$$ squares, which gives 2601 squares. Merging four $$2 \times 2$$ squares into one $$4 \times 4$$ square reduces the count by 3, and $$2601 - 2007 = 594 = 3 \times 198$$. So merge 198 disjoint $$2 \times 2$$ blocks of these squares (there is room for $$25 \times 25 = 625$$), giving 198 squares of side 4 and $$2601 - 792 = 1809$$ squares of side 2, i.e. 2007 squares in all.